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A little geometry gives simple expressions
for the horizontal and vertical position errors on the zerooffset section,
which are to be corrected by migration.
Figure 2 defines the
required quantities for a reflection event recorded at S corresponding
to the reflectivity at R.
reflkine
Figure 2
Geometry of the normal ray of length d and the vertical ``shaft''
of length z for
a zerooffset experiment above a dipping reflector.

 
The twoway travel time for the event is
related to the length d of the normal ray by
 
(1) 
where v is the constant propagation velocity.
Geometry of the triangle CRS shows
that the true depth of the reflector at R is given by
 
(2) 
and the lateral shift between true position C and false position S
is given by
 
(3) 
It is conventional to rewrite equation (2) in terms of twoway
vertical traveltime :
 
(4) 
Thus both the vertical shift and the horizontal shift are seen to vanish when the dip angle is zero.
Next: Hand migration
Up: MIGRATION DEFINED
Previous: A dipping reflector
Stanford Exploration Project
12/26/2000